P = ( X A − )2 + ( X B − )2 = | X – A | + | X – B | ≥ | X – A + B – X | = B – A (A < B)

258. Ta cĩ : P = ( x a )

2

+ ( x b )

2

= | x – a | + | x – b | ≥ | x – a + b – x | = b – a (a < b).

Dấu đẳng thức xảy ra khi (x – a)(x – b) ≥ 0 ⇔ a ≤ x ≤ b. Vậy min P = b – a ⇔ a ≤ x ≤ b.